Question

Divide 3 – 2x + 2x2 by (2-x) and verify the division algorithm.​

Answer 1

Step-by-step explanation:

degree (-x+2). <br>

quotient = (-2x-3) and remainder = 9 <br>

(quotient

divisor) + remainder <br>

<br>

<br>

<br>

<br> = dividend. <br> Thus, (quotient

divisor)+ remainder = dividend. <br> Hence, the division algorithm is verified.

Answer 2

Step-by-step explanation:

Given :-

3 - 2x + 2x²

To find :-

Divide 3-2x + 2x² by (2-x) and verify the division algorithm.

Solution :-

Given Polynomial is 3-2x+2x²

On writing it in the standard form 2x²-2x+3

2-x can be written as -x+2

On dividing 2x²-2x+3 by (-x+2) then

-x+2 ) 2x²-2x+3 (-2x -2

2x²-4x

(-) (+)

__________

0 +2x +3

2x -4

(-) (+)

___________

7

____________

Quotient = -2x-2

Remainder = 7

Check :-

We know that

Division Algorithm on Polynomials is

p(x) = g(x)×q(x) +r(x)

Now on taking RHS

=> g(x)×q(x) +r(x)

=> (2-x) ×(-2x-2) + 7

=> 2(-2x-2) -x(-2x-2) +7

=> -4x-4 +2x²+2x+7

=> 2x²+(2x-4x)+(7-4)

=> 2x²-2x+3

=> 3-2x+2x²

=> Given Polynomial

Verified the given relations in the given problem

Answer :-

Quotient = -2x-2

Remainder = 7

Used formulae:-

Division Algorithm on Polynomials is

p(x) = g(x)×q(x) +r(x)

Where , p(x) = Dividend

• g(x) = Divisor
• q(x)=quotient
• r(x)=remainder